# Zachary Kudlak, PhD

**Assistant Professor**

PhD, University of Rhode Island

**Office: **Howard Hall, Room 241

**Phone: **732-571-4454

**Email: **zkudlak@monmouth.edu

**Fall 2015 Office Hours: **

Monday: 2:50 - 4:10 p.m.

Wednesday: 1:15 - 2:35 p.m.

Thursday: 10:05 - 11:25 a.m.

**Fall 2015 Courses: **

Mathematical Modeling in the Social Sciences

Real Analysis

**Research Interests: **

Many of my research interests lie in the field of graph theory. A graph is a set of objects, which we call vertices, along with a set of pairs of these objects, which we call edges. A natural way to picture a graph is to draw the vertices as dots, and then draw an edge between two vertices by drawing an arc from one vertex to the other. We can see that graphs can define many of the structures that we interact with in the world. For example, a graph could be made up of vertices, which represent people that belong to a social network, and two vertices could be connected by an edge if the two people are friends in this social network. Other applications come from areas including computer science, biology, chemistry, scheduling, and sociology. Because of these many varied applications, graph theory is a particularly useful area of mathematics to study. I am interested in studying different properties of graphs.

**Professional Associations: **

American Mathematical Society

Mathematical Association of America

International Society of Difference Equations

Young Mathematicians Network

**Awards: **

Phi Beta Kappa, May 2004

Robert Sine Memorial Award for Teaching Excellence in Mathematics, May 2009

Editor for the Young Mathematicians Network, August 2012 - Present

Faculty Judge at the Undergraduate Poster Session at the Joint Mathematics Meetings, Boston, MA, 2012

John B. Fraleigh Prize for Undergraduate Excellence in Mathematics, May 2004

Pi Mu Epsilon, National Mathematics Honor Society, May 2003

Kappa Delta Pi, International Honor Society in Education, May 2003

The University of Rhode Island Alumni Association Award for Outstanding Junior, May 2003

Competed in the 2004 William Lowell Putnam Mathematical Competition, December 2004

## Selected Works:

**Scholarly Articles: **

E. Drymonis, Y. Kostrov and Z. Kudlak, On Rational Difference Equations with Periodic Coefficients, International

Journal of Difference Equations, Volume 7 no.1 (2012), 19-34.

M. Bellavia, E. Camouzis, Z. Kudlak, G. Ladas, On the Boundedness Character of Rational Equations, Part 3,

Journal of Difference Equations and Applications, Volume 13 (2007), 479-524.

**Presentations/Invited Talks: **

On the Boundedness Character of a System of Rational Difference Equations in the Plane with Nonnegative

Periodic Coefficients, 2013 Joint Mathematics Meetings, San Diego, CA, January 9-12, 2013.

Modeling Bodies of Revolution in Calculus, 2013 Joint Mathematics Meetings, San Diego, CA, January 9-12, 2013.

Using Difference Equations as a Vector for Undergraduate Research, 2012 Trends in Undergraduate Research in Mathematical Sciences Conference, Chicago, IL, October 26-28, 2012.

On Systems of Rational Difference Equations with Periodic Coefficients, 2012 Fall Sectional Meeting of the AMS, Rochester, NY, September 22-23, 2012. (Invited)

Poster:"Exponential and Poisson Random Variables in a Campus Cafeteria", PosterFest at the 2012 MAA MathFest, Madison, WI, August 2-4,2012.

On Rational Difference Equations with Periodic Coefficients, 2012 International Conference on Difference Equations and Applications, Barcelona, Spain, July 23-27, 2012.

On Rational Difference Equations with Periodic Coefficients, Part II, 2012 Spring Eastern Sectional Meeting of the AMS,George Washington University, Washington, D.C., March 17-18, 2012. (Invited)

On Rational Difference Equations with Periodic Coefficients, 2012 Joint Mathematics Meetings, Boston, MA, January 4-7, 2012.

On a (p, q)-Edge Coloring of Kn, 2011 Joint Mathematics Meetings, New Orleans, LA, January 6-9, 2011.

On a (6, 5)-Edge Coloring of Kn, 41st Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, FL, March 8 - 12, 2010.

On a (5, 4)-Edge Coloring of Kn, 22nd Cumberland Conference on Combinatorics, Graph Theory, and Computing, Western Kentucky University, Bowling Green, KY, May 21 - 23, 2009.

**Invited Talks for Students:**

SIAM/AWM Lecture Series, State University of New York at New Paltz, NY, November 14, 2012.

Structure in Numbers, an Introduction to Ramsey Theory, a lecture for the Math Club, Siena College, Loudonville, NY, November 2, 2012.

What is it like to study mathematics? A short introduction to Graph Theory, La Salle Academy, Providence, RI, May 22, 2008.

**Forthcoming: **